This study material is designed specifically for the Quantitative Aptitude section of the RBI Grade B Phase 1 exam, where percentages often appear in data interpretation, profit/loss, and direct calculation problems. Percentages test your speed and accuracy in conversions, increases/decreases, and comparisons. Drawing from reliable sources and exam patterns up to 2025, this guide covers everything from basics to advanced tricks. Practice daily to master it—aim for solving 5-10 questions in under 5 minutes.

1. Introduction to Percentages

Percentage means “per hundred” (from Latin “per centum”). It represents a part of a whole expressed as a fraction of 100. For RBI Grade B, percentages are crucial in topics like profit/loss, simple/compound interest, data interpretation (bar graphs, pie charts), and ratios.

• Basic Definition:
  If you score 400 out of 500,
  your percentage is (400/500) × 100 = 80%.
  
• Why Important for RBI Grade B?: Questions often involve successive changes, elections, populations, or salaries. Expect 2-5 direct/indirect questions in Phase 1 Quant (out of 30 marks).

2. Key Concepts and Formulas

Understand these fundamentals before shortcuts. Use them for accurate calculations.

Concept/Formula	Description	Example
Basic Percentage	(Part/Whole) × 100	20 out of 50 = (20/50) × 100 = 40%
Percentage to Fraction/Decimal	Divide by 100 (e.g., 25% = 25/100 = 1/4 = 0.25)	75% = 3/4 or 0.75
Fraction to Percentage	Multiply by 100 (e.g., 3/5 × 100 = 60%)	2/7 × 100 ≈ 28.57%
Ratio to Percentage	Convert to fraction first (e.g., 2:5 = 2/5 × 100 = 40%)	3:4 = 75%
Percentage Increase	[(New – Original)/Original] × 100	Price from ₹100 to ₹120: (20/100) × 100 = 20% increase
Percentage Decrease	[(Original – New)/Original] × 100	Price from ₹100 to ₹80: (20/100) × 100 = 20% decrease
Net Change After Successive Percentages	For two changes a% and b%: a + b + (a×b)/100	+10% then +20%: 10 + 20 + (10×20)/100 = 32%
Reverse Percentage (Original from Final)	For x% increase: Original = Final / (1 + x/100)	Final ₹120 after 20% increase: 120 / 1.2 = ₹100
Product Constancy	If A increases by x%, B decreases by [x/(100+x)] × 100% to keep A×B constant	Speed up 20%, time down [20/120] × 100 ≈ 16.67% for same distance
Population Formula	P after n years at r%: P × (1 + r/100)^n	1000 at 5% for 2 years: 1000 × (1.05)^2 = 1102.5
A% of B = B% of A	Swap for easier calc	18% of 50 = 50% of 18 = 9

Memorize common equivalents: 1/2=50%, 1/3≈33.33%, 1/4=25%, 1/5=20%, 1/8=12.5%, 1/10=10%, 1/20=5%.

3. Shortcuts and Tricks

These are time-savers for RBI Grade B’s time-bound Quant section (30 questions in 25-30 mins effectively).

1. Breakdown Trick: Split into 10%, 5%, 1% for quick mental math.
   • 10% = divide by 10 (e.g., 10% of 250=25).
   • 5% = half of 10% (12.5).
   • 1% = divide by 100 (2.5).
   • Example: 47% of 200 = 40% (80) + 7% (14) = 94. How: 40%=4×10%, 7%=7×1%.
     
2. Numerator Swapping: x% of y = y% of x.
   • Example: 20% of 50 = 50% of 20=10.
     
3. Doubling/Halving: For 20%=double 10%, 5%=half 10%, 40%=double 20%.
   • Example: 5% of 300=15 (half of 30=10% of 300).
     
4. Successive Changes Quick Calc: For a% then b%: Final multiplier = (1 + a/100) × (1 + b/100).
   • Example: +10% then -5%: 1.1 × 0.95=1.045 (4.5% increase).
     
5. Fractional Breakdown: Use equivalents like 12.5%=1/8, 16.67%=1/6.
   • Example: 87.5% of 1600=1600 – (1600/8)=1400.
     
6. Reverse for Original: After x% decrease, original = final / (1 – x/100).
   • Example: ₹45 after 25% decrease: 45 / 0.75=₹60.
     
7. Quick Estimate: Round for approx (e.g., 19% of 47≈20% of 50=10).
   • Useful for DI approximations.
     
8. Error Percentage: (Error/Correct) × 100.
   • Example: Measured 105 instead of 100: (5/100)×100=5%.

Practice these mentally—RBI questions reward speed.

4. Solved Examples

These illustrate concepts with step-by-step reasoning.

Example 1: Basic Calculation
Question: An agent sells goods worth ₹15,000 and gets 12.5% commission. What’s the commission?
Solution: Commission = 12.5% of 15,000 = (12.5/100) × 15,000 = (1/8) × 15,000 = ₹1,875.
(How: 12.5%=1/8; divide 15,000 by 8.)

Example 2: Successive Changes
Question: Book price increases 10%, then decreases 5%. Net change?
Solution: Assume ₹100. After +10%: ₹110. After -5%: 0.95×110=₹104.5. Net +4.5%.
Formula: 10 – 5 + (10×-5)/100 = 5 – 0.5=4.5% increase.

Example 3: Reverse Percentage
Question: Man loses 20% of money, spends 25% of remainder, left with ₹480. Original amount?
Solution: Let original=x. After -20%: 0.8x. Spend 25% of that: left 75% of 0.8x=0.6x=480. x=480/0.6=₹800.

Example 4: Fraction Increase
Question: Numerator +100%, denominator +200%, new fraction=4/21. Original fraction?
Solution: Let original=x/y. New: 2x/3y=4/21. Cross-multiply: 42x=12y → x/y=12/42=2/7.

Example 5: Population
Question: Population 1000 increases 5% annually for 2 years. Final?
Solution: 1000 × (1.05)^2=1000×1.1025=1102.5.

5. Practice Questions with Solutions

Solve these 10 questions (mix of easy-medium). Explain steps for closed-ended math.

1. Question: 50% of (x-y)=30% of (x+y). What % of x is y?
   Options: a)20% b)25% c)30% d)40%
   Solution: 0.5(x-y)=0.3(x+y). 0.5x-0.5y=0.3x+0.3y. 0.2x=0.8y. y/x=0.2/0.8=0.25=25%. Answer: b.
   (How: Subtract 0.3x from both sides, add 0.5y: 0.2x=0.8y.)
2. Question: One-eighth of a number is 17.25. 73% of number?
   Solution: Number=17.25×8=138. 73% of 138=138×0.73=100.74.
   (How: 70%=96.6, 3%=4.14, total 100.74.)
3. Question: Salary increases 10% yearly. June 2011: ₹22,385. June 2009 salary?
   Solution: Let 2009=x. 2010=x×1.1. 2011=1.1x×1.1=1.21x=22,385. x=22,385/1.21≈18,500.
   (How: Reverse compound: Divide by (1.1)^2.)
4. Question: Numerator +400%, denominator +500%, new=10/21. Original fraction?
   Solution: New: 5x/6y=10/21. 105x=60y. x/y=60/105=4/7.
   (How: Cross-multiply and simplify.)
5. Question: Travel P to Q at 40 kmph, return 50% faster. Avg speed?
   Solution: Return=60 kmph. Avg= (2×40×60)/(40+60)=48 kmph.
   (How: Harmonic mean for equal distance.)
6. Question: A number ×7 is as much above 260 as original below 260. 32% of original?
   Solution: Let x below 260: 260-x. 7x=260+(260-x)=520-x. 8x=520. x=65. Original=260-65=195? Wait, correct: Let original=y. 7y – 260 = 260 – y. 8y=520. y=65. 32% of 65=20.8.
   (How: Set equation for symmetry.)
7. Question: 1/8 of number=17.25. 73%? (Repeat for practice: 100.74.)
8. Question: Fraction numerator +25%, denominator +20%, becomes 5/6. Original x/y?
   Solution: 1.25x/1.2y=5/6. 1.25x= (5/6)×1.2y. Simplify: x/y=0.8.
   (How: Cross and divide.)
9. Question: Maya salary 60% > Swevi. EMI equal, Swevi EMI=20% salary=₹30,000. Maya EMI+rent=half salary. Savings?
   Solution: Swevi=1.5L (30k=20%). Maya=2.4L. EMI=30k. Rent=3×30k=90k (from half=120k total exp). Savings=2.4L-1.2L=1.2L.
   (How: Let ratios, solve x=3.)
10. Question: Cost S=20% > T (T cost=8000). S transport=500, 12% loss. SP S?
    Solution: S cost=9600. Total=10100. SP=88% of 10100=8888.
    (How: Loss means SP=CP×0.88.)

6. Previous Year Questions with Solutions

From RBI Grade B (2019-2022). Focus on patterns like salaries, fractions.

1. RBI 2022: Maya salary 60% > Swevi… (As in practice 9). Savings=₹120,000.
   Solution: As above.
2. RBI 2021: Cost S=20% > T… SP S=₹8888.
   Solution: As above.
3. RBI 2019: Number ×7 above 260 as below… 32% original=20.8.
   Solution: As in example 6.
4. RBI 2022 Q2: Election: A,B contest, 25% no vote, 1200 invalid, valid=60,000, A wins by 20%. A votes?
   Solution: Total voters= (60k +1200)/75% =82,400. Valid=60k. A wins by 20% of valid=12k. A=(60k+12k)/2=36k.
   (How: Invalid=2% valid, no vote=25%, so valid=73% total.)
5. RBI 2018: 40% voters no vote… Similar election logic.
   Solution: Work backward from valid votes.

7. Tips for RBI Grade B Exam

• Time Management: Use shortcuts for DI (e.g., approx % in graphs).
• Common Pitfalls: Confuse “by x%” vs “to x%”. Always assume base=100 for quick checks.
• Practice Strategy: Solve 50 questions/week. Review PYQs from 2018-2024. Use apps for timed mocks.
• Resources: Refer to RBI site for patterns. Supplement with Quant books like R.S. Aggarwal.
• Exam Day: For percentages in DI, calculate 10%/1% first. Aim 80% accuracy in Quant.